My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance


Reply
 
LinkBack Thread Tools Display Modes
October 17th, 2012, 01:53 AM   #1
Senior Member
 
Joined: Sep 2012

Posts: 112
Thanks: 0

application of differentiation in economics

A monopolist produces x units of a commodity at a total cost of ax^2+bx+c and the demand law for the same is given by
p= Q-Rx, where Q and R constants.
A tax of Rs.K per unit is levied by the government. The manufacturer adds the tax to his cost.

(a) find the price and the output both before and after tax.
(b) show that the tax brings in maximum return when K=(Q-b)/2

I could solve the 1st question i.e. (a). But I don't know how to solve (b). Please help.
helloprajna is offline  
 
October 17th, 2012, 10:39 AM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: application of differentiation in economics

Tax is maximized when the derivative of tax revenue is 0. First solve for tax revenue, then differentiate. Next set this equal to zero and solve. Finally, substitute back into the original.
CRGreathouse is offline  
October 17th, 2012, 11:00 PM   #3
Senior Member
 
Joined: Sep 2012

Posts: 112
Thanks: 0

Re: application of differentiation in economics

Quote:
Originally Posted by CRGreathouse
Tax is maximized when the derivative of tax revenue is 0. First solve for tax revenue, then differentiate. Next set this equal to zero and solve. Finally, substitute back into the original.
Does that mean 'maximum return' refers to 'maximum total tax revenue' here???
helloprajna is offline  
October 18th, 2012, 07:25 AM   #4
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: application of differentiation in economics

Yes.
CRGreathouse is offline  
October 28th, 2012, 09:37 AM   #5
Senior Member
 
Joined: Sep 2012

Posts: 112
Thanks: 0

Re: application of differentiation in economics

Quote:
Originally Posted by CRGreathouse
Yes.
Thank you so much....
helloprajna is offline  
Reply

  My Math Forum > Science Forums > Economics

Tags
application, differentiation, economics



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Application of differentiation Tear_Grant Calculus 3 April 15th, 2015 10:15 AM
application of differentiation in economics helloprajna Economics 1 October 16th, 2012 01:29 AM
application of differentiation in economics helloprajna Economics 7 October 16th, 2012 01:16 AM
Application Of Derivatives in Commerce and Economics Ansh Agrawal Economics 8 February 13th, 2012 02:24 AM
Differentiation application Ronaldo Complex Analysis 3 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.